MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Stanford Mathematics Tournament
2010 Stanford Mathematics Tournament
10
SMT 2010 Algebra #10
SMT 2010 Algebra #10
Source:
February 11, 2012
algebra
polynomial
Vieta
Problem Statement
Find the sum of all solutions of the equation
1
x
2
−
1
+
2
x
2
−
2
+
3
x
2
−
3
+
4
x
2
−
4
=
2010
x
−
4
\frac{1}{x^2-1}+\frac{2}{x^2-2}+\frac{3}{x^2-3}+\frac{4}{x^2-4}=2010x-4
x
2
−
1
1
+
x
2
−
2
2
+
x
2
−
3
3
+
x
2
−
4
4
=
2010
x
−
4
Back to Problems
View on AoPS